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Marc Y. R Henrion

Malawi Liverpool Wellcome Trust Clinical Research Programme, Liverpool School of Tropical Medicine



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Angeziwa Chirambo

Malawi Liverpool Wellcome Trust Clinical Research Programme, London School of Hygiene and Tropical Medicine



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Ndaru Jambo

Malawi Liverpool Wellcome Trust Clinical Research Programme



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Tonney S. Nyirenda

Malawi Liverpool Wellcome Trust Clinical Research Programme, College of Medicine, University of Malawi



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Melita A. Gordon

Malawi Liverpool Wellcome Trust Clinical Research Programme, University of Liverpool



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163 – SPEED: Longitudinal/Correlated Data

Mixed Latent Markov Models for Longitudinal Multiple Diagnostics Data With an Application to Salmonella in Malawi

Sponsor: Biometrics Section
Keywords: latent Markov model, mixed model, latent variable model, Bayesian modelling, random effects, Salmonella

Marc Y. R Henrion

Malawi Liverpool Wellcome Trust Clinical Research Programme, Liverpool School of Tropical Medicine

Angeziwa Chirambo

Malawi Liverpool Wellcome Trust Clinical Research Programme, London School of Hygiene and Tropical Medicine

Ndaru Jambo

Malawi Liverpool Wellcome Trust Clinical Research Programme

Tonney S. Nyirenda

Malawi Liverpool Wellcome Trust Clinical Research Programme, College of Medicine, University of Malawi

Melita A. Gordon

Malawi Liverpool Wellcome Trust Clinical Research Programme, University of Liverpool

Latent Markov models (LMMs) are commonly used to analyze longitudinal data from multiple diagnostic tests. LMMs consist of a structural model for the latent infection state, defining probabilities for the initial state and transmission between states, and a measurement model for the observed test results, defining the item response probabilities and thus test sensitivities and specificities. LMMs typically assume that tests are independent conditional on the latent infection state. This is likely to be violated for tests using similar technologies. We introduce random effects to relax the conditional independence assumption and we derive a generalization of the basic LMM for an application to Salmonella infection data. We analyze longitudinal data from four molecular PCR tests and a stool culture test from patients in Blantyre, Malawi. To assess the tests' performances, we consider basic and mixed LMMs, both with time homogeneous and heterogeneous transition probabilities. We compare the different models and discuss technical considerations. A PCR assay using primers from the TTR gene achieves the best sensitivity / specificity trade-off.

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